00:01
Here in this problem, we are told that the velocity of a particle is given by t squared plus 4t plus 1.
00:13
We're also told the initial position time t equals 0 is 6.
00:19
And we want to find a few different things.
00:23
Now, first, we want to find a position at any given time.
00:27
Now, our position is the integral of velocity, and so we're going to integrate our velocity here to get our position.
00:34
Anti -derivative of t squared is one -third t cubed anti -derivative of 4t is 2 t squared anti -derivative of 1 is t and then we have plus c we find c by using our initial condition here we know f of zero if we plug in zero everywhere for t that that'll be six inside just tells us that c is six and so let's come back up there and replace c with six and so here's our position at any time t on b we want the position at time t equals 4.
01:25
And so all this means to do is plug in 4 for t.
01:33
And so again, all we did here was just plug in 4 everywhere for t.
01:37
And then now we're going to evaluate this.
01:44
And then we do, this should give us about 63 .3 repeat...